Mechanics Test

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Mechanics Test - 1

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Question 1

1 / -0

Match the following:

List - I	List - II
(1) Planck's constant	(A) [ML^-1T^-2]
(2) Gravitational constant	(B) [ML^-1T^-1]
(3) Bulk modulus	(C) [ML²T^-1]
(4) Coefficient of viscosity	(D) [M^-1L³T^-2]

(1) - (C), (2) - (D), (3) - (A), (4) - (B)

(1) - (B), (2) - (A), (3) - (C), (4) - (D)

(1) - (C), (2) - (B), (3) - (A), (4) - (D)

(1) - (C), (2) - (D), (3) - (B), (4) - (A)

Solution

Dimensions of Planck's constant = [ML²T^-1]

Dimensions of gravitational constant = [M^-1L³T^-2]

Dimensions of bulk modulus = [ML^-1T^-2]

Dimensions of coefficients of viscosity = [ML^-1T^-1]

Question 2
1 / -0

Which of the following quantities is unitless as well as dimensionless?

A
Angle

B
Solid angle

C
Mechanical equivalent of heat

D
Refractive index

Solution

In optics, the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as the ratio of the speed of light in vacuum relative to that in the considered medium. This can be written mathematically as:
n = speed of light in a vacuum/speed of light in a medium
Since refractive index is the ratio of same quantities, so it has no unit and is a dimensionless quantity.
Question 3
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The pair(s) of physical quantities that do(es) not have the same dimensions is/are

A
Reynolds number and coefficient of friction

B
Curie and frequency of a light wave

C
latent heat and gravitational potential

D
Planck's constant and torque

Solution

Reynolds number and coefficient of friction are dimensionless quantities.
Curie is the number of atoms decaying per unit time and frequency is the number of oscillations per unit time. Latent heat and gravitational potential both have the same dimensions corresponding to L²T^-2.
Question 4
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Which of the following sets of quantities has the same dimensional formula?

A
Frequency, angular frequency and angular momentum

B
Surface tension, stress and spring constant

C
Acceleration, momentum and retardation

D
Work, energy and torque

Solution

As the work is defined as the dot product of force and displacement.
Torque is represented as the cross product of radius and the force.
Energy is defined as the capacity of doing work so work , energy and the torque has same dimensions.